Question

for each set of three lengths, determine if they can be the side lengths of a triangle.

lengths	can be side lengths of a triangle	cannot be side lengths of a triangle
11, 6, 15	o	o
13.0, 3.6, 10.3	o	o
9, 20, 15	o	o

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check 7, 7, 25

$7 + 7=14<25$, so it cannot be side - lengths of a triangle.

Step3: Check 11, 6, 15

$11 + 6 = 17>15$, $11+15 = 26>6$, $6 + 15=21>11$, so it can be side - lengths of a triangle.

Step4: Check 13.0, 3.6, 10.3

$3.6+10.3 = 13.9>13.0$, $3.6 + 13.0=16.6>10.3$, $10.3+13.0 = 23.3>3.6$, so it can be side - lengths of a triangle.

Step5: Check 9, 20, 15

$9+15 = 24>20$, $9 + 20=29>15$, $15+20 = 35>9$, so it can be side - lengths of a triangle.

Answer:

7, 7, 25: Cannot be side lengths of a triangle
11, 6, 15: Can be side lengths of a triangle
13.0, 3.6, 10.3: Can be side lengths of a triangle
9, 20, 15: Can be side lengths of a triangle